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\(\cfrac{4\sqrt{3}}{2 - \sqrt{2}} - \cfrac{30}{4\sqrt{3} - \sqrt{18}} - \cfrac{\sqrt{18}}{3 - \sqrt{12}}\) \(= \cfrac{4\sqrt{3}(2 + \sqrt{2})}{(2 - \sqrt{2})(2 + \sqrt{2})} - \cfrac{30(4\sqrt{3} + \sqrt{18})}{(4\sqrt{3} - \sqrt{18})(4\sqrt{3} + \sqrt{18})} - \cfrac{\sqrt{18}(3 + \sqrt{12})}{(3 - \sqrt{12})(3 + \sqrt{12})}\) \(= \cfrac{4\sqrt{3}(2 + \sqrt{2})}{4 - 2} - \cfrac{30(4\sqrt{3} + \sqrt{3×3×2})}{48 - 18} - \cfrac{\sqrt{3×3×2}(3 + \sqrt{2×2×3})}{9 - 12}\) \(= \cfrac{4\sqrt{3}(2 + \sqrt{2})}{2} - \cfrac{30(4\sqrt{3} + 3\sqrt{2})}{30} - \cfrac{3\sqrt{2}(3 + 2\sqrt{3})}{-3}\) \(= 2\sqrt{3}(2 + \sqrt{2}) - (4\sqrt{3} + 3\sqrt{2}) + \sqrt{2}(3 + 2\sqrt{3})\) \(= 4\sqrt{3} + 2\sqrt{6} - 4\sqrt{3} - 3\sqrt{2} + 3\sqrt{2} + 2\sqrt{6}\) \(= 4\sqrt{6}\) (Answer)